Variance Calculation Quiz: Calculating Variance (Basic Level)

  • 9th Grade
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| Questions: 20 | Updated: Dec 16, 2025
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1) What is the first step to find the variance of a data set?

Explanation

Variance measures how much data varies around the mean. To calculate it, you first need the mean (average). Example: For data {2, 4, 6}, Mean = (2 + 4 + 6) ÷ 3 = 12 ÷ 3 = 4.

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About This Quiz
Variance Calculation Quiz: Calculating Variance (Basic Level) - Quiz

Ever wondered how far numbers drift from their average? This quiz walks you through basic variance problems that show how spread works within a data set. You’ll compare values, measure deviations, and see how variance captures the consistency of a group. A simple set of questions helps you build strong... see moreintuition step by step.
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2) After finding the mean, what should you do next?

Explanation

The next step is to find each deviation from the mean. Example with {5, 7, 9}, Mean = 7 → Deviations = 5 - 7 = -2, 7 - 7 = 0, 9 - 7 = 2.

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3) Why do we square each deviation?

Explanation

Deviations can be negative or positive, and adding them gives zero. Squaring removes negatives and shows actual spread. For example, -3 and 3 both become 9 after squaring.

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4) Variance is the __________ of the squared deviations.

Explanation

Steps: 1. Find mean 2. Find deviations 3. Square each deviation 4. Take the average of the squared deviations.

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5) Find the population variance for {3, 4, 5}.

Explanation

Mean = 4; Deviations = -1, 0, 1; Squares = 1, 0, 1; Population variance = (1 + 0 + 1) ÷ 3 = 0.67.

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6) Variance can be negative.

Explanation

Since deviations are squared, results can never be negative. The lowest possible variance is 0 (when all data points are identical).

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7) Find the population variance for data {5, 7, 9, 11}.

Explanation

Mean = 8; Deviations = -3, -1, 1, 3; Squares = 9, 1, 1, 9; Sum = 20; Variance = 20 ÷ 4 = 5.

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8) For data {8, 10, 12}, the population variance is __________ (round to 2 decimals).

Explanation

Mean = 10; Deviations = -2, 0, 2; Squares = 4, 0, 4; Variance = (4 + 0 + 4) ÷ 3 = 2.67.

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9) If all values are equal, what is the variance?

Explanation

When all values are identical, deviations are 0, so variance = 0.

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10) Select all correct steps for calculating population variance.

Explanation

Population variance = Sum of squared deviations ÷ total number of data points (n).

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11) Which mistake leads to variance = 0 when it shouldn’t?

Explanation

Adding raw deviations cancels positives and negatives. Always square before averaging.

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12) Find the sample variance for {4, 7, 9}. Round to 2 decimals.

Explanation

Mean = 6.67; Deviations = -2.67, 0.33, 2.33; Squares = 7.11, 0.11, 5.43; Sum = 12.65; Sample variance = 12.65 ÷ 2 = 6.33.

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13) For data {1, 2, 3, 6}, the population variance is __________.

Explanation

Mean = 3; Deviations = -2, -1, 0, 3; Squares = 4, 1, 0, 9; Variance = (4 + 1 + 0 + 9) ÷ 4 = 3.50.

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14) For a sample, variance is calculated by dividing by n − 1.

Explanation

Using n − 1 (Bessel’s correction) makes sample variance a better population estimate.

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15) Two classes have test scores: A: {70,72,73,75} B: {60,70,80,90}. Which class has the higher variance?

Explanation

Class B’s scores are spread further apart (60–90), so its variance is larger.

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16) Which statements about variance are true?

Explanation

Variance measures spread, is always non-negative, and equals 0 only when all data points are identical.

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17) Find the population variance for {0, 2, 4, 6}.

Explanation

Mean = 3; Deviations = -3, -1, 1, 3; Squares = 9, 1, 1, 9; Variance = 20 ÷ 4 = 5.

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18) For data {2, 3, 7}, a student added deviations to get 0 and said variance = 0. The correct population variance is __________.

Explanation

Mean = 4; Deviations = -2, -1, 3; Squares = 4, 1, 9; Variance = 14 ÷ 3 = 4.67.

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19) Find the sample variance for {10, 12, 15}. Round to 2 decimals.

Explanation

Mean = 12.33; Deviations = -2.33, -0.33, 2.67; Squares = 5.43, 0.11, 7.11; Sample variance = 12.65 ÷ 2 = 6.33.

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20) Which of the following are correct steps to find sample variance?

Explanation

Sample variance = (Sum of squared deviations) ÷ (n − 1). It adjusts for bias in small samples.

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What is the first step to find the variance of a data set?
After finding the mean, what should you do next?
Why do we square each deviation?
Variance is the __________ of the squared deviations.
Find the population variance for {3, 4, 5}.
Variance can be negative.
Find the population variance for data {5, 7, 9, 11}.
For data {8, 10, 12}, the population variance is __________ (round to...
If all values are equal, what is the variance?
Select all correct steps for calculating population variance.
Which mistake leads to variance = 0 when it shouldn’t?
Find the sample variance for {4, 7, 9}. Round to 2 decimals.
For data {1, 2, 3, 6}, the population variance is __________.
For a sample, variance is calculated by dividing by n − 1.
Two classes have test scores: A: {70,72,73,75} B: {60,70,80,90}. Which...
Which statements about variance are true?
Find the population variance for {0, 2, 4, 6}.
For data {2, 3, 7}, a student added deviations to get 0 and said...
Find the sample variance for {10, 12, 15}. Round to 2 decimals.
Which of the following are correct steps to find sample variance?
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